In recent years model-based reasoning has achieved a certain prominence among logicians and cognitive scientists. Its repute is deserved, notwithstanding that it has some vigorous rivals. Although both model-based and non-model-based systems aim at elucidations of good reasoning, there are certain issues that challenge them equally across the lines of their respective theoretical and methodolog...

Syllogism reasoning is a common and important form of in human thinking from Aristotle onwards. To overcome the shortcomings previous studies, this article makes full use set theory classical propositional logic, deduces remaining 23 valid syllogisms only on basis syllogism EIO-2 perspective mathematical structuralism, then successfully establishes concise formal axiom system for categorical sy...

N.B.: For the references, please see Selected Bibliography on Aristotle's Theory of Categorical Syllogism "When modem logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle’s contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotl...

We consider two categorical syllogisms, valid or invalid, to be equivalent if they can be transformed into each other by certain transformations, going back to Aristotle, that preserve validity. It is shown that two syllogisms are equivalent if and only if they have the same models. Counts are obtained for the number of syllogisms in each equivalence class. To make the development more natural,...

It is generally accepted that it is a mistake that Aristotle ignore the moods of the fourth figure in his syllogism. In this paper, I shall argue the Aristotelian syllogism consisting of the essential moods and their derivative moods is complete or self-contained, all the moods of the fourth figure can be derived from the essential moods. The analysis table provided in the paper will contribute...